Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
Author: James Stewart
Publisher: Cengage Learning
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Chapter 2, Problem 8RCC
(a)
To determine
To state: The power rule.
(b)
To determine
To state: The constant multiple rule.
(c)
To determine
To state: The
(d)
To determine
To state: The
(e)
To determine
To state: The product rule.
(f)
To determine
To state: The
(g)
To determine
To state: The chain rule.
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Chapter 2 Solutions
Essential Calculus: Early Transcendentals
Ch. 2.1 - (a) Find the slope of the tangent line to the...Ch. 2.1 - (a) Find the slope of the tangent line to the...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - (a) Find the slope of the tangent to the curve y =...Ch. 2.1 - (a) Find the slope of the tangent to the curve...Ch. 2.1 - The graph shows the position function of a car....Ch. 2.1 - Shown are graphs of the position functions of two...
Ch. 2.1 - If a ball is thrown into the air with a velocity...Ch. 2.1 - If an arrow is shot upward on the moon with a...Ch. 2.1 - The displacement (in meters) of a particle moving...Ch. 2.1 - The displacement (in meters) of a particle moving...Ch. 2.1 - Prob. 15ECh. 2.1 - Find an equation of the tangent line to the graph...Ch. 2.1 - If an equation of the tangent tine to the curve y...Ch. 2.1 - If the tangent line to y= f(x) at (4, 3) passes...Ch. 2.1 - Sketch the graph of a function f for which f(0) =...Ch. 2.1 - Sketch the graph of a function g for which g(0) =...Ch. 2.1 - If f(x) = 3x2 x3 , find f'(l) and use it to find...Ch. 2.1 - Prob. 22ECh. 2.1 - (a) If F(x) = 5x/(l + x2), find F'(2) and use it...Ch. 2.1 - Prob. 24ECh. 2.1 - Find f'(a). f(x) = 3x2 4x + 1Ch. 2.1 - Find f'(a). f(t) = 2t3 + tCh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - 3136 Each limit represents the derivative of some...Ch. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - The number N of US cellular phone subscribers (in...Ch. 2.1 - The number N of locations of a popular coffeehouse...Ch. 2.1 - Prob. 41ECh. 2.1 - If a cylindrical tank holds 100,000 gallons of...Ch. 2.1 - The cost of producing x ounces of gold from a new...Ch. 2.1 - The number of bacteria after r hours in a...Ch. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - The graph shows the influence of the temperature T...Ch. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Match the graph of each function in (a)(d) with...Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Shown is the graph of the population function P(t)...Ch. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - The unemployment rate U(t) varies with time. The...Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - The graph of f is given. State, with reasons, the...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Use the definition of a derivative to find f'(x)...Ch. 2.2 - Prob. 42ECh. 2.2 - If f(x) = 2x2 x3, find f'(x), f"(x), f'"(x), and...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Where is the greatest integer function f(x) = [[ x...Ch. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.3 - Differentiate the function. f(x) = 240Ch. 2.3 - Differentiate the function. f(x)=2Ch. 2.3 - Differentiate the function. f(t)=223tCh. 2.3 - Differentiate the function. F(x)=34x8Ch. 2.3 - Prob. 5ECh. 2.3 - Differentiate the function. f(t) = 1.4t5 2.5t2+...Ch. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Differentiate the function. B(y) = cy6Ch. 2.3 - Differentiate the function. A(s)=12s5Ch. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Differentiate the function. y=x(x1)Ch. 2.3 - Prob. 17ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 18ECh. 2.3 - Differentiate the function. z=Ay10+BcosyCh. 2.3 - Prob. 22ECh. 2.3 - Differentiate the function. y=x2+4x+3xCh. 2.3 - Differentiate the function. y=sin2+cCh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 55ECh. 2.3 - Find the points on the curve y = 2x3 + 3x2 12x +...Ch. 2.3 - Prob. 37ECh. 2.3 - Show that the curve y = 6x3 + 5x 3 has no tangent...Ch. 2.3 - Find an equation of the tangent line to the curve...Ch. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 65ECh. 2.3 - Prob. 64ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 66ECh. 2.3 - For what values of a and b is the line 2x + y = b...Ch. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Draw a diagram showing two perpendicular lines...Ch. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - If a ball is thrown vertically upward with a...Ch. 2.3 - If a rock is thrown vertically upward from the...Ch. 2.3 - The position function of a particle is given by s...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 51ECh. 2.3 - The cost function for production of a commodity is...Ch. 2.4 - Find the derivative of f(x) = (1 + 2x2)(x x2) in...Ch. 2.4 - Find the derivative o f the function...Ch. 2.4 - Differentiate. g(t)=t3costCh. 2.4 - Differentiate. f(x)=xsinxCh. 2.4 - Differentiate. g(x)=1+2x34xCh. 2.4 - Differentiate. G(x)=x222x+1Ch. 2.4 - Differentiate. h()=csccotCh. 2.4 - Differentiate. J(v) = (v3 2v)(v4 + v2)Ch. 2.4 - Prob. 5ECh. 2.4 - Differentiate. y=sincosCh. 2.4 - Differentiate. y=x31x2Ch. 2.4 - Differentiate. y=x+1x3+x2Ch. 2.4 - Differentiate. y=v32vvvCh. 2.4 - Differentiate. g(t)=ttt1/3Ch. 2.4 - Differentiate. f(t)=2t2+tCh. 2.4 - Differentiate. y=x1x+1Ch. 2.4 - Differentiate. f()=sec1+secCh. 2.4 - Differentiate. y=1secxtanxCh. 2.4 - Prob. 24ECh. 2.4 - Differentiate. f(x)=xx+cxCh. 2.4 - Find an equation of the tangent line to the given...Ch. 2.4 - Find an equation of the tangent line to the given...Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - If f and g are the functions whose graphs are...Ch. 2.4 - Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F...Ch. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 7ECh. 2.4 - Differentiate. y = 2 sec x csc xCh. 2.4 - Prob. 19ECh. 2.4 - Differentiate. y=cosx1sinxCh. 2.4 - Prob. 23ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Find an equation of the tangent line to the curve...Ch. 2.4 - Prob. 30ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 40ECh. 2.4 - A mass on a spring vibrates horizontally on a...Ch. 2.4 - Prob. 52ECh. 2.4 - Prob. 36ECh. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Find the derivative of the function. F(x) = (x4 +...Ch. 2.5 - Find the derivative of the function. F(x) = (4x ...Ch. 2.5 - Find the derivative of the function. F(x)=12xCh. 2.5 - Find the derivative of the function....Ch. 2.5 - Prob. 11ECh. 2.5 - Find the derivative of the function. f(t)=1+tant3Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Find the derivative of the function. f(x) = (2x ...Ch. 2.5 - Find the derivative of the function. g(x) = (x2 +...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Find the derivative of the function. y=(x2+1x21)3Ch. 2.5 - Find the derivative of the function. f(s)=s2+1s2+4Ch. 2.5 - Find the derivative of the function. y=sin(xcosx)Ch. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Find the derivative of the function. y = cot2(sin...Ch. 2.5 - Prob. 36ECh. 2.5 - 742 Find the derivative of the function. 37....Ch. 2.5 - Find the derivative of the function. y=x+x+xCh. 2.5 - Prob. 39ECh. 2.5 - 742 Find the derivative of the function. 40....Ch. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - A table of values for f, g, f, and g is given. (a)...Ch. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 75ECh. 2.5 - Prob. 76ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - Air is being pumped into a spherical weather...Ch. 2.5 - Prob. 72ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 74ECh. 2.5 - Use the Chain Rule to show that if is measured in...Ch. 2.5 - Prob. 78ECh. 2.5 - Prob. 77ECh. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - Find dy/dx by implicit differentiation. x3 + y3 =...Ch. 2.6 - Find dy/dx by implicit differentiation. 2x3 + x2y ...Ch. 2.6 - Prob. 5ECh. 2.6 - Find dy/dx by implicit differentiation. y5 + x2y3...Ch. 2.6 - Find dy/dx by implicit differentiation. 11. y cos...Ch. 2.6 - Find dy/dx by implicit differentiation. 12....Ch. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Find dy/dx by implicit differentiation. x+y=1+x2y2Ch. 2.6 - 3-16 Find dy/dx by implicit differentiation. 13....Ch. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Find dy/dx by implicit differentiation. 20....Ch. 2.6 - Prob. 17ECh. 2.6 - If g(x) + x sin g(x) = x2, find g(0).Ch. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 19ECh. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 22ECh. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 24ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Find the points on the lemniscate in Exercise 23...Ch. 2.6 - Show by implicit differentiation that the tangent...Ch. 2.6 - Show that the sum of the x-and y-intercepts of any...Ch. 2.6 - Prob. 41ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 49ECh. 2.6 - Prob. 50ECh. 2.7 - Prob. 1ECh. 2.7 - (a) If A is the area of a circle with radius r and...Ch. 2.7 - Prob. 3ECh. 2.7 - The length of a rectangle is increasing at a rate...Ch. 2.7 - A cylindrical tank with radius 5 m is being filled...Ch. 2.7 - The radius of a sphere is increasing at a rate of...Ch. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - A particle is moving along a hyperbola xy = 8. As...Ch. 2.7 - Prob. 13ECh. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - Two cars start moving from the same point. One...Ch. 2.7 - A spotlight on the ground shines on a wall 12m...Ch. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 24ECh. 2.7 - A trough is 10 ft long and its ends have the shape...Ch. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 37ECh. 2.7 - A lighthouse is located on a small island 3 km...Ch. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.8 - Find the linearization L(x) of the function at a....Ch. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 10ECh. 2.8 - 7-10 Verify the given linear approximation at a =...Ch. 2.8 - Prob. 8ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 17ECh. 2.8 - Let y = tan x. (a) Find the differential dy. (b)...Ch. 2.8 - Let y = tan x. (a) Find the differential dy. (b)...Ch. 2.8 - Prob. 11ECh. 2.8 - Prob. 14ECh. 2.8 - Use a linear approximation (or differentials) to...Ch. 2.8 - Prob. 13ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 21ECh. 2.8 - Prob. 22ECh. 2.8 - The circumference of a sphere was measured to be...Ch. 2.8 - Prob. 24ECh. 2.8 - One side of a right triangle is known to be 20 cm...Ch. 2.8 - Prob. 25ECh. 2.8 - When blood flows along a blood vessel, the flux F...Ch. 2.8 - Prob. 28ECh. 2.8 - Prob. 29ECh. 2.8 - Suppose that we dont have a formula for g(x) but...Ch. 2 - Prob. 1RCCCh. 2 - Prob. 2RCCCh. 2 - Prob. 4RCCCh. 2 - Prob. 3RCCCh. 2 - Prob. 5RCCCh. 2 - Prob. 6RCCCh. 2 - Prob. 7RCCCh. 2 - Prob. 1RQCh. 2 - Prob. 8RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 63RECh. 2 - Prob. 7RECh. 2 - Prob. 9RECh. 2 - Prob. 8RECh. 2 - Prob. 8RCCCh. 2 - Prob. 9RCCCh. 2 - Prob. 10RCCCh. 2 - Prob. 11RCCCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Prob. 4RQCh. 2 - Prob. 5RQCh. 2 - Prob. 6RQCh. 2 - Prob. 12RQCh. 2 - Prob. 7RQCh. 2 - Prob. 11RQCh. 2 - Prob. 9RQCh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 19RECh. 2 - Prob. 33RECh. 2 - Prob. 1RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 18RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 24RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 39RECh. 2 - Prob. 35RECh. 2 - Prob. 32RECh. 2 - Prob. 34RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - 70. If f and g are the functions whose graphs are...Ch. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 57RECh. 2 - Prob. 56RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 65RECh. 2 - Prob. 64RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Evaluate limx01+tanx1+sinxx3.Ch. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RE
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- 4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward
- 3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả B X C d) ẢB°C e) ẢX B XC.arrow_forward
- 3.13 (B). A beam ABC, 6 m long, is simply-supported at the left-hand end A and at B I'm from the right-hand end C. The beam is of weight 100 N/metre run. (a) Determine the reactions at A and B. (b) Construct to scales of 20 mm = 1 m and 20 mm = 100 N, the shearing-force diagram for the beam, indicating thereon the principal values. (c) Determine the magnitude and position of the maximum bending moment. (You may, if you so wish, deduce the answers from the shearing force diagram without constructing a full or partial bending-moment diagram.) [C.G.] C240 N, 360 N, 288 Nm, 2.4 m from A.]arrow_forward5. Using parentheses make sense of the expression V · VXVV · Å where Ả = Ã(x, y, z). Is the result a vector or a scaler?arrow_forward3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20 KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m. Calculate the value of the reactions at A and D and hence draw the S.F. and B.M. diagrams. What are the magnitude and position of the maximum B.M. on the beam? [41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J m,arrow_forward
- 3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A, a second concentrated load of 20 KN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine: (a) the values of the reactions at B and 0, (6) the position and magnitude of the maximum bending moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]arrow_forward3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward3.11 (B). A beam, 12 m long, is to be simply supported at 2m from each end and to carry a U.d.l of 30kN/m together with a 30 KN point load at the right-hand end. For ease of transportation the beam is to be jointed in two places, one joint being Situated 5 m from the left-hand end. What load (to the nearest KN) must be applied to the left-hand end to ensure that there is no B.M. at the joint (i.e. the joint is to be a point of contraflexure)? What will then be the best position on the beam for the other joint? Determine the position and magnitude of the maximum B.M. present on the beam. [114 KN, 1.6 m from r.h. reaction; 4.7 m from 1.h. reaction; 43.35 KN m.]arrow_forward
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